The generation interval (the time between infection of primary and secondary cases) and its often used proxy, the serial interval (the time between symptom onset of primary and secondary cases) are critical parameters in understanding infectious disease dynamics. Because it is difficult to determine who infected whom, these important outbreak characteristics are not well understood for many diseases. We present a novel method for estimating transmission intervals using surveillance or outbreak investigation data that, unlike existing methods, does not require a contact tracing data or pathogen whole genome sequence data on all cases. We start with an expectation maximization algorithm and incorporate relative transmission probabilities with noise reduction. We use simulations to show that our method can accurately estimate the generation interval distribution for diseases with different reproductive numbers, generation intervals, and mutation rates. We then apply our method to routinely collected surveillance data from Massachusetts (2010-2016) to estimate the serial interval of tuberculosis in this setting.